首次积分与(n+1)维多重sine-Gordon方程的无穷序列新解

J4 ›› 2017, Vol. 34 ›› Issue (3): 316-326.

首次积分与(n+1)维多重sine-Gordon方程的无穷序列新解

套格图桑

内蒙古师范大学数学科学学院，内蒙古呼和浩特 010022

收稿日期:2016-02-24 修回日期:2016-04-26 出版日期:2017-05-28 发布日期:2017-05-22

The first integral and new infinite sequence solutions of (n+1)-dimensional multiple sine-Gordon equation

College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

Received:2016-02-24 Revised:2016-04-26 Published:2017-05-28 Online:2017-05-22

摘要/Abstract

摘要： 通过几种函数变换把(n+1)维多重sine-Gordon方程的求解转化为常微分方程组的求解。利用常微分方程组的首次积分与可求解几种常微分方程的B?cklund变换和解的非线性叠加公式，构造了(n+1)维多重sine-Gordon方程的无穷序列类孤子新解。

关键词: 首次积分； (n+1)维多重sine-Gordon方程；B?cklund变换；无穷序列类孤子新解

Abstract: The solution of (n+1)-dimensional multiple sine-Gordon equation is transformed into solution of the set of ordinary differential equations by several function transformations. New infinite sequence soliton-like solutions of (n+1)-dimensional multiple sine-Gordon equation are constructed by combining the first integrals of the set of ordinary differential equations with B?cklund transformation and the nonlinear superposition formula of solutions to several kinds of solvable ordinary differential equations.

Key words: the first integral; (n+1)-dimensional multiple sine-Gordon equation; B?cklund transformation; new infinite sequence soliton-like solutions

中图分类号:

O175.29

套格图桑. 首次积分与(n+1)维多重sine-Gordon方程的无穷序列新解[J]. J4, 2017, 34(3): 316-326.

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